Mathematical Knowledge for Teaching Proof in Secondary Mathematics Teacher Preparation

Abstract

Proof is considered foundational for mathematical understanding and has received increased attention in mathematics education over the last two decades. This mixed methods research study explores opportunities to develop mathematical knowledge for teaching proof during secondary mathematics teacher preparation. I used the mathematical knowledge for teaching proof framework (Lesseig, 2011) to develop a survey distributed to secondary mathematics methods instructors. This survey provided data pertaining to each instructor’s learning goals around proof and instructional strategies they use to support opportunities to develop their teacher candidates’ mathematical knowledge for teaching proof. In addition, interviews were conducted with five participants to provide further details on their survey responses and their instructional strategies. The responses related to learning goals were often focused on providing opportunities to develop common content knowledge for proof. The findings also indicated that factors such as educational level and departmental assignment were not associated with providing opportunities intended to support the development of mathematical knowledge for teaching proof. Instead, a teacher educator’s approach towards proof in their methods course(s) is influenced by their view of what counts as proof. This view varied across all participants and is not unlike the variation discovered in previous research. Further research must explore reasonable expectations for what counts as proof at the secondary level and must identify specific strategies for drawing connections between common content knowledge for proof and the work of teaching.